Breaking of parallelograms in presence of torsion: an equivalent alternative approach to detect gravitational waves

The equations for gravitational plane waves produced by a typical binary system as a solution of linear approximation of Einstein equations is derived. The dynamics of the corresponding gravitational field is analyzed in a 4-dimensional space-time manifold, endowed with a metric and taking into account the torsion. In this context, the geometrical reason of the existence of torsion due to the presence of gravitational waves, as an asymmetry of connection coefficients with respect of the swapping of indices's is highlighted. In a laser interferometer gravitational detector The delay time between the arrivals of the two laser beams traveling back and forth along the two arms of in presence of gravitational waves, is interpreted from this point of view. The geometrical interpretation of torsion, links this delay time to the breaking of the parallelogram formed by the trajectories of the laser beams in space-time. This delay is calculated for a typical NS-NS binary pulsar in two specific orientations with respect of the experimental device, corresponding to different polarizations of the gravitational waves. These values are related to the relative length variation of the detector's arms in presence of gravitational waves, and shown to be completely equivalent to the results obtained in the context of the standard General Relativity.